Problem: Simplify the following expression: $ y = \dfrac{9}{-2t - 3} - \dfrac{1}{5} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{5}{5}$ $ \dfrac{9}{-2t - 3} \times \dfrac{5}{5} = \dfrac{45}{-10t - 15} $ Multiply the second expression by $\dfrac{-2t - 3}{-2t - 3}$ $ \dfrac{1}{5} \times \dfrac{-2t - 3}{-2t - 3} = \dfrac{-2t - 3}{-10t - 15} $ Therefore $ y = \dfrac{45}{-10t - 15} - \dfrac{-2t - 3}{-10t - 15} $ Now the expressions have the same denominator we can simply subtract the numerators: $y = \dfrac{45 - (-2t - 3) }{-10t - 15} $ Distribute the negative sign: $y = \dfrac{45 + 2t + 3}{-10t - 15}$ $y = \dfrac{2t + 48}{-10t - 15}$ Simplify the expression by dividing the numerator and denominator by -1: $y = \dfrac{-2t - 48}{10t + 15}$